detailed information: The input equation set is: Question solving process:
Multiply both sides of equation (1) by 2 Divide the two sides of equation (1) by 3, the equation can be obtained: , then subtract both sides of equation (6) from both sides of equation (2), the equations are reduced to:
Multiply both sides of equation (1) by 2 Divide the two sides of equation (1) by 3, the equation can be obtained: , then subtract both sides of equation (7) from both sides of equation (4), the equations are reduced to:
| | | | | | - | 2 3 | B | | - | 2 3 | C | + | | D | + | | 2 | E | = | | 0 | | (4) |
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Divide the two sides of equation (1) by 3, the equation can be obtained: , then subtract both sides of equation (8) from both sides of equation (5), the equations are reduced to:
| | | | | | - | 2 3 | B | | - | 2 3 | C | + | | D | + | | 2 | E | = | | 0 | | (4) |
| - | 1 3 | B | | - | 1 3 | C | + | | 3 | D | + | | E | = | | 0 | | (5) |
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Multiply both sides of equation (2) by 9 Divide the two sides of equation (2) by 4, the equation can be obtained: , then subtract both sides of equation (9) from both sides of equation (3), the equations are reduced to:
| | | | | | - | 2 3 | B | | - | 2 3 | C | + | | D | + | | 2 | E | = | | 0 | | (4) |
| - | 1 3 | B | | - | 1 3 | C | + | | 3 | D | + | | E | = | | 0 | | (5) |
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Divide the two sides of equation (2) by 2, the equation can be obtained: , then add the two sides of equation (10) to both sides of equation (4), the equations are reduced to:
| | | | | | | - | 1 3 | B | | - | 1 3 | C | + | | 3 | D | + | | E | = | | 0 | | (5) |
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Divide the two sides of equation (2) by 4, the equation can be obtained: , then add the two sides of equation (11) to both sides of equation (5), the equations are reduced to:
Multiply both sides of equation (3) by 2 Divide the two sides of equation (3) by 5, the equation can be obtained: , then add the two sides of equation (12) to both sides of equation (4), the equations are reduced to:
Divide the two sides of equation (3) by 5, the equation can be obtained: , then add the two sides of equation (13) to both sides of equation (5), the equations are reduced to:
Multiply both sides of equation (4) by 3, the equation can be obtained: , then subtract both sides of equation (14) from both sides of equation (5), the equations are reduced to:
Multiply both sides of equation (5) by 2 Divide both sides of equation (5) by 5, get the equation:, then add the two sides of equation (15) to both sides of equation (4), get the equation:
Multiply both sides of equation (4) by 5 Divide both sides of equation (4) by 4, get the equation:, then add the two sides of equation (16) to both sides of equation (3), get the equation:
Subtract both sides of equation (4) from both sides of equation (2), get the equation:
Multiply both sides of equation (3) by 4 Divide both sides of equation (3) by 15, get the equation:, then add the two sides of equation (17) to both sides of equation (2), get the equation:
Multiply both sides of equation (3) by 2 Divide both sides of equation (3) by 5, get the equation:, then subtract both sides of equation (18) from both sides of equation (1), get the equation:
Multiply both sides of equation (2) by 3 Divide both sides of equation (2) by 4, get the equation:, then subtract both sides of equation (19) from both sides of equation (1), get the equation:
The coefficient of the unknown number is reduced to 1, and the equations are reduced to:
Therefore, the solution of the equation set is:
解方程组的详细方法请参阅:《多元一次方程组的解法》 |